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Math Help - A^-1 and a proof help

  1. #1
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    A^-1 and a proof help

    Hello guys, I've been trying to solve this problem all night and was wondering if I could get some help.

    1. Suppose A is nxn nonsingular. Prove Det(A^-1) = 1 / Det(A)
    I was trying to use the formula A^-1 = 1 / det(A) * adj(A) but had no luck

    2. A = | 1/2 -1/2 | find A^-1
    | 1/2x 1/2x|

    I keep getting
    1 1/x
    -1 x
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  2. #2
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    Quote Originally Posted by sleepiiee View Post
    Hello guys, I've been trying to solve this problem all night and was wondering if I could get some help.

    1. Suppose A is nxn nonsingular. Prove Det(A^-1) = 1 / Det(A)
    I was trying to use the formula A^-1 = 1 / det(A) * adj(A) but had no luck

    2. A = | 1/2 -1/2 | find A^-1
    | 1/2x 1/2x|

    I keep getting
    1 1/x
    -1 x

    AA^{-1} = I

    \det{(AA^{-1})} = \det{(I)}

    \det{(A)}\det{(A^{-1})} = 1

    \det{(A^{-1})} = \frac{1}{\det{(A)}}.
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